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The question asks which graph represents two functions, \( h(x) \) and \( j(x) \), that are decreasing across all points of the domain common to both functions.

### Step-by-step Analysis:
1. **Key Idea:** A function is decreasing in an interval if, as \( x \) increases within that interval, the function's value decreases.

2. **Common Domain:** 
   - The graphs show a specific interval where both functions overlap. In that interval, both \( h(x) \) and \( j(x) \) need to be decreasing for the graph to satisfy the condition.

3. **Graph Observations:**
   - **First graph:** \( h(x) \) (blue curve) is decreasing in the left half of the domain, but \( j(x) \) (orange curve) is increasing, disqualifying this graph.
   - **Second graph:** \( h(x) \) is decreasing where it overlaps with \( j(x) \), and \( j(x) \) is also decreasing within their common domain.
   - **Third graph:** \( h(x) \) is decreasing, but \( j(x) \) is increasing in the common domain.
   - **Fourth graph:** \( h(x) \) is decreasing, but \( j(x) \) is increasing in the common domain.

### Correct Answer:
The **second graph** satisfies the condition where both \( h(x) \) and \( j(x) \) are decreasing across the domain common to both functions.

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Would you like a more detailed explanation of how I analyzed the graphs or why specific graphs are disqualified?

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Here are 5 related questions for further exploration:
1. What mathematical methods can you use to determine whether a function is decreasing from its equation?
2. How can you find the common domain of two functions algebraically?
3. Can two functions be decreasing over disjoint intervals and still satisfy a similar condition?
4. How does the derivative help determine whether a function is decreasing or increasing?
5. What happens if one function is constant in the common domain—does that count as "decreasing"?

**Tip:** Remember, a decreasing function always has a negative slope or derivative in the interval of interest!

Which graph represents two functions that are decreasing on all points across the domain that is common to both functions?

Analyze graphs to determine which represents two functions that are decreasing across their common domain. Learn key concepts in functions, domains, and decreasing intervals. Suitable for students in Grades 9-11.

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